Thus an "apple" in our records is a unit of measurement, the quantity in question being "number of apples"

This evolves into simple arithmetic

1 apple added to 1 apple is 2 apples

10 apples subtracted from 30 apples is 20 apples

Introduction of shorthand notation

Mathematics can discard the physical objects in question and has the luxury of concerning itself with abstract concepts

Whereas in mathematics the constant represents a numerical constant, in physics this constant can represent a physical constant, thereby allowing physical objects to behave as mathematical entities in mathematical equations

Units of measurements are important in mathematical equations since they represent critical information and errors in calculations will result if these physical constants are neglected

is wrong in the sense that
is the only answer allowed under the rules of mathematics

Also, care must be taken when we perform mathematical operations

represents 9 apples arranged in a square

creates a new physical quantity apple(orange) that is neither apples nor oranges! This is how new physical quantities, i.e. energy are created from lengths, times, and masses.